(* Content-type: application/vnd.wolfram.mathematica *)

(*** Wolfram Notebook File ***)
(* http://www.wolfram.com/nb *)

(* CreatedBy='Mathematica 8.0' *)

(*CacheID: 234*)
(* Internal cache information:
NotebookFileLineBreakTest
NotebookFileLineBreakTest
NotebookDataPosition[       157,          7]
NotebookDataLength[     22523,        556]
NotebookOptionsPosition[     20956,        507]
NotebookOutlinePosition[     21301,        522]
CellTagsIndexPosition[     21258,        519]
WindowFrame->Normal*)

(* Beginning of Notebook Content *)
Notebook[{

Cell[CellGroupData[{
Cell["PressureReducingValveG", "Section",
 CellChangeTimes->{{3.4785828348125*^9, 3.47858284740625*^9}, 
   3.47867904165625*^9, {3.483026885*^9, 3.483026890359375*^9}, 
   3.4988885288318987`*^9, {3.507886987593746*^9, 3.507887015359016*^9}, 
   3.507887177638189*^9, {3.572724409593012*^9, 3.572724410652072*^9}}],

Cell[BoxData[
 RowBox[{"<<", "C:\\\\Hopsan\\Compgen\\CompgenNG.mx"}]], "Input",
 CellChangeTimes->{{3.5772037650720577`*^9, 3.5772037650780582`*^9}, {
  3.611474457184202*^9, 3.611474523938877*^9}, {3.6114745588913717`*^9, 
  3.61147456057154*^9}}],

Cell[BoxData[
 RowBox[{
  RowBox[{"path", "=", 
   RowBox[{"ToFileName", "[", 
    RowBox[{"{", 
     RowBox[{
     "\"\<C:\>\"", ",", "\"\<HopsanTrunk\>\"", ",", 
      "\"\<ComponentLibraries\>\"", ",", "\"\<defaultLibrary\>\"", ",", 
      "\"\<Hydraulic\>\"", ",", "\"\<Special\>\""}], "}"}], "]"}]}], 
  ";"}]], "Input",
 CellChangeTimes->{{3.5757727777685804`*^9, 3.575772792541806*^9}, {
   3.5757728423954945`*^9, 3.5757728498367076`*^9}, {3.57577333888545*^9, 
   3.5757733706315055`*^9}, 3.5757734316206255`*^9, 3.6031909973287797`*^9, 
   3.6057717887213297`*^9, {3.605771829393656*^9, 3.605771830929744*^9}, 
   3.6058530990363216`*^9, {3.621138851005574*^9, 3.621138863716845*^9}}],

Cell[CellGroupData[{

Cell["System model", "Subsection",
 CellChangeTimes->{{3.504161099890625*^9, 3.504161102453125*^9}}],

Cell[BoxData[{
 RowBox[{
  RowBox[{"domain", "=", "\"\<Hydraulic\>\""}], ";"}], "\n", 
 RowBox[{
  RowBox[{"displayName", "=", "\"\<PressureReducingValveG\>\""}], ";"}], "\n", 
 RowBox[{
  RowBox[{
  "brief", "=", 
   "\"\<A hydraulic pressure relief valve based on geometry\>\""}], 
  ";"}], "\n", 
 RowBox[{
  RowBox[{"componentType", "=", "\"\<ComponentQ\>\""}], ";"}], "\n", 
 RowBox[{
  RowBox[{"author", "=", "\"\<Petter Krus <petter.krus@liu.se>\>\""}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
  "affiliation", " ", "=", " ", 
   "\"\<Division of Fluid and Mechatronic Systems, Link\[ODoubleDot]ping \
University\>\""}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"SetFilenames", "[", 
   RowBox[{"path", ",", "domain", ",", "displayName"}], "]"}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"ResetComponentVariables", "[", "]"}], ";"}]}], "Input",
 CellChangeTimes->{{3.503905077842648*^9, 3.503905079842648*^9}, {
   3.5039103076641607`*^9, 3.5039103985397425`*^9}, {3.5039164662834997`*^9, 
   3.5039164750178747`*^9}, {3.5039165143772497`*^9, 
   3.5039165189397497`*^9}, {3.5041051675625*^9, 3.504105226359375*^9}, {
   3.507570546125*^9, 3.507570569546875*^9}, {3.507570601046875*^9, 
   3.50757067696875*^9}, 3.507796401609375*^9, {3.507887022343302*^9, 
   3.507887057967846*^9}, {3.5078871702320337`*^9, 3.507887175028847*^9}, {
   3.5158208831437864`*^9, 3.51582092036206*^9}, 3.52267078596875*^9, {
   3.5727244220517244`*^9, 3.5727244258479414`*^9}, 3.5758601094265933`*^9}],

Cell[BoxData[
 RowBox[{
  RowBox[{"nodeConnections", "=", 
   RowBox[{"{", "\[IndentingNewLine]", 
    RowBox[{
     RowBox[{"HydraulicQnode", "[", 
      RowBox[{"1", ",", 
       RowBox[{"1.", "*", 
        RowBox[{"10", "^", "5"}]}], ",", "\"\<Upstream port\>\""}], "]"}], 
     ",", "\[IndentingNewLine]", 
     RowBox[{"HydraulicQnode", "[", 
      RowBox[{"2", ",", 
       RowBox[{"1.", "*", 
        RowBox[{"10", "^", "5"}]}], ",", "\"\<Downstream port\>\""}], "]"}]}],
     "\[IndentingNewLine]", "}"}]}], ";"}]], "Input",
 CellChangeTimes->{{3.4752292939381866`*^9, 3.4752293318441935`*^9}, {
   3.47808399728125*^9, 3.478083998921875*^9}, 3.4988885288475237`*^9, {
   3.50394176215625*^9, 3.503941811890625*^9}, {3.507576389140625*^9, 
   3.507576508765625*^9}, {3.50757655321875*^9, 3.507576570375*^9}, {
   3.507796238859375*^9, 3.50779624034375*^9}, {3.5156830475625*^9, 
   3.515683050984375*^9}, {3.538136856098759*^9, 3.5381369597752786`*^9}, {
   3.5719055396181374`*^9, 3.5719055424261427`*^9}}],

Cell[BoxData[
 RowBox[{
  RowBox[{"inputVariables", "=", 
   RowBox[{"{", "\[IndentingNewLine]", 
    RowBox[{"{", 
     RowBox[{"pref", ",", 
      RowBox[{"1.", "*", 
       RowBox[{"10", "^", "7"}]}], ",", "double", ",", "\"\<Pa\>\"", ",", 
      "\"\<Reference pressure\>\""}], "}"}], "\[IndentingNewLine]", "}"}]}], 
  ";"}]], "Input",
 CellChangeTimes->{{3.5381369657755475`*^9, 3.5381370104181724`*^9}}],

Cell[BoxData[
 RowBox[{
  RowBox[{
   RowBox[{"outputVariables", "=", 
    RowBox[{"{", "\[IndentingNewLine]", 
     RowBox[{"{", 
      RowBox[{
      "xv", ",", "0.", ",", "double", ",", "\"\<m\>\"", ",", 
       "\"\<Spool position\>\""}], "}"}], "\[IndentingNewLine]", "}"}]}], 
   ";"}], " "}]], "Input",
 CellChangeTimes->{{3.5381369720414534`*^9, 3.5381369916673326`*^9}, {
  3.57772189105064*^9, 3.577721891954692*^9}}],

Cell[BoxData[
 RowBox[{
  RowBox[{"inputParameters", "=", 
   RowBox[{"{", "\[IndentingNewLine]", 
    RowBox[{
     RowBox[{"{", 
      RowBox[{
      "rho", ",", "860.", ",", "double", ",", "\"\<kg/m3\>\"", ",", 
       "\"\<oil density\>\""}], "}"}], ",", "\[IndentingNewLine]", 
     RowBox[{"{", 
      RowBox[{
      "visc", ",", "0.03", ",", "double", ",", "\"\<Ns/m2\>\"", ",", 
       "\"\<viscosity \>\""}], "}"}], ",", "\[IndentingNewLine]", 
     RowBox[{"{", 
      RowBox[{
      "Dv", ",", "0.01", ",", "double", ",", "\"\<m\>\"", ",", 
       "\"\<Spool diameter\>\""}], "}"}], ",", "\[IndentingNewLine]", 
     RowBox[{"{", 
      RowBox[{
      "frac", ",", "0.1", ",", "double", ",", "\"\<\>\"", ",", 
       "\"\<Fraction of spool opening\>\""}], "}"}], ",", 
     "\[IndentingNewLine]", 
     RowBox[{"{", 
      RowBox[{
      "Bv", ",", "1000.", ",", "double", ",", "\"\<N/(m s)\>\"", ",", 
       "\"\<Damping\>\""}], "}"}], ",", "\[IndentingNewLine]", 
     RowBox[{"{", 
      RowBox[{
      "Xvmax", ",", "0.002", ",", "double", ",", "\"\<m\>\"", ",", 
       "\"\<Max spool displacement\>\""}], "}"}], ",", "\[IndentingNewLine]", 
     RowBox[{"{", 
      RowBox[{
      "Cq", ",", "0.67", ",", "double", ",", "\"\< \>\"", ",", 
       "\"\<Flow coefficient\>\""}], "}"}], ",", "\[IndentingNewLine]", 
     RowBox[{"{", 
      RowBox[{
      "phi", ",", "1.17", ",", "double", ",", "\"\<rad\>\"", ",", 
       "\"\<Stream angle\>\""}], "}"}], ",", "\[IndentingNewLine]", 
     RowBox[{"{", 
      RowBox[{
      "ks", ",", "10000.", ",", "double", ",", "\"\<N/m\>\"", ",", 
       "\"\<Spring constant\>\""}], "}"}], ",", "\[IndentingNewLine]", 
     RowBox[{"{", 
      RowBox[{
      "p0", ",", "100000.", ",", "double", ",", "\"\<Pa\>\"", ",", 
       "\"\<Turbulent pressure trans.\>\""}], "}"}]}], "\[IndentingNewLine]", 
    "}"}]}], ";"}]], "Input",
 CellGroupingRules->{GroupTogetherGrouping, 10000.},
 CellChangeTimes->{{3.4779981058619356`*^9, 3.4779981542683554`*^9}, 
   3.4780017782035847`*^9, {3.478002203430644*^9, 3.478002217153696*^9}, {
   3.478002277203772*^9, 3.4780023021490927`*^9}, {3.4780026209521627`*^9, 
   3.478002664340765*^9}, {3.478021796078125*^9, 3.478021842203125*^9}, {
   3.478021885296875*^9, 3.47802199571875*^9}, {3.47802539628125*^9, 
   3.478025479125*^9}, {3.478026054375*^9, 3.47802606034375*^9}, {
   3.47818056640625*^9, 3.47818064359375*^9}, {3.478184752578125*^9, 
   3.478184788859375*^9}, {3.4781848254375*^9, 3.47818487890625*^9}, {
   3.47818496809375*^9, 3.478184980140625*^9}, {3.478189354859375*^9, 
   3.478189379078125*^9}, {3.478679541453125*^9, 3.478679542*^9}, 
   3.47868324640625*^9, 3.478683514703125*^9, {3.4807602098503075`*^9, 
   3.480760210147073*^9}, {3.480760285603793*^9, 3.4807602892909627`*^9}, 
   3.480760331584048*^9, 3.483026964640625*^9, {3.483027180765625*^9, 
   3.483027244046875*^9}, {3.4873878032782784`*^9, 3.4873878199976707`*^9}, 
   3.4988223817958884`*^9, 3.4988885288318987`*^9, {3.5023520516875*^9, 
   3.50235222190625*^9}, {3.50235391759375*^9, 3.50235391940625*^9}, 
   3.503905029342648*^9, 3.5039111089927917`*^9, {3.503914664843855*^9, 
   3.503914668218855*^9}, {3.50391516520323*^9, 3.503915204718855*^9}, {
   3.5039967133130913`*^9, 3.5039967163764143`*^9}, {3.5039969681607733`*^9, 
   3.503996993616342*^9}, {3.507574582234375*^9, 3.507574588828125*^9}, {
   3.507576286109375*^9, 3.507576354453125*^9}, {3.5077959019375*^9, 
   3.507795944828125*^9}, {3.51568580440625*^9, 3.51568581115625*^9}, 
   3.5159285657593565`*^9, {3.573147641136273*^9, 3.5731476559331193`*^9}, {
   3.5731482493080587`*^9, 3.5731482508341455`*^9}, {3.6180818304459014`*^9, 
   3.6180818626187415`*^9}, {3.6180821152711926`*^9, 3.618082115437202*^9}, 
   3.6180821470030074`*^9}],

Cell[BoxData[
 RowBox[{
  RowBox[{"ke", "=."}], ";", 
  RowBox[{"kf", "=."}], ";"}]], "Input",
 CellChangeTimes->{{3.577729430347863*^9, 3.5777294365572186`*^9}}],

Cell[BoxData[
 RowBox[{
  RowBox[{"localExpressions", "=", 
   RowBox[{"{", "\[IndentingNewLine]", 
    RowBox[{
     RowBox[{"Av", "==", 
      FractionBox[
       RowBox[{"pi", " ", 
        SuperscriptBox["Dv", "2"]}], "4"]}], ",", "\[IndentingNewLine]", 
     RowBox[{"w", "==", 
      RowBox[{"pi", " ", "frac", " ", "Dv", " ", 
       RowBox[{"Sin", "[", "phi", "]"}]}]}]}], "\[IndentingNewLine]", "}"}]}],
   ";"}]], "Input",
 CellChangeTimes->{{3.483027001578125*^9, 3.483027021109375*^9}, {
   3.4873877137123394`*^9, 3.487387727322237*^9}, 3.4988885288318987`*^9, {
   3.503914893406355*^9, 3.50391490070323*^9}, {3.50391509367198*^9, 
   3.503915095406355*^9}, {3.525772523916875*^9, 3.525772528510625*^9}, {
   3.534756520505298*^9, 3.534756559181628*^9}, {3.534756692025055*^9, 
   3.534756695744233*^9}, {3.57190456751803*^9, 3.571904619278921*^9}, {
   3.573148310137538*^9, 3.5731483108905807`*^9}, 3.573149708071495*^9, {
   3.5731497755273533`*^9, 3.5731497796395884`*^9}}],

Cell[BoxData[{
 RowBox[{
  RowBox[{"kf", "=", 
   RowBox[{"2", " ", "Cq", " ", "w", " ", 
    RowBox[{"Cos", "[", "phi", "]"}], " ", 
    RowBox[{"(", 
     RowBox[{"p1", "-", "p2"}], ")"}]}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"ke", "=", 
   RowBox[{"ks", "+", "kf"}]}], ";"}]}], "Input",
 CellChangeTimes->{{3.573149714210846*^9, 3.5731497291246986`*^9}, {
  3.573149782505752*^9, 3.573149788960121*^9}}],

Cell[BoxData[
 RowBox[{
  RowBox[{"systemEquationsDA", "=", " ", 
   RowBox[{"{", "\[IndentingNewLine]", 
    RowBox[{
     RowBox[{
      RowBox[{
       RowBox[{"Bv", " ", 
        RowBox[{"der", "[", " ", "xv", "]"}]}], " ", "+", 
       RowBox[{"ke", " ", "xv"}]}], " ", "==", 
      RowBox[{
       RowBox[{"(", 
        RowBox[{"pref", "-", "p2"}], ")"}], "Av"}]}], ",", 
     "\[IndentingNewLine]", 
     RowBox[{"q2", "==", 
      RowBox[{"xv", "*", "Cq", " ", "w", " ", 
       SqrtBox[
        FractionBox["2.", "rho"]], 
       RowBox[{"signedSquareL", "[", 
        RowBox[{
         RowBox[{"p1", "-", "p2"}], ",", "p0"}], "]"}]}]}]}], "}"}]}], 
  ";"}]], "Input",
 CellChangeTimes->{{3.478679350421875*^9, 3.4786793594375*^9}, {
   3.47867939090625*^9, 3.478679416*^9}, 3.483026918*^9, 
   3.4873877224157987`*^9, 3.4988885288318987`*^9, {3.5039967325838947`*^9, 
   3.5039967690624475`*^9}, {3.504104403484375*^9, 3.50410440521875*^9}, {
   3.5075701360625*^9, 3.507570153265625*^9}, {3.507570213453125*^9, 
   3.507570214015625*^9}, {3.5075703420625*^9, 3.507570342109375*^9}, 
   3.5076079715712585`*^9, {3.507796204234375*^9, 3.50779621396875*^9}, {
   3.507887076139488*^9, 3.5078870785613317`*^9}, {3.5719046338649464`*^9, 
   3.571904651898578*^9}, 3.571904682880233*^9, {3.572724506299543*^9, 
   3.5727245105057836`*^9}}],

Cell[BoxData[
 RowBox[{
  RowBox[{"systemBoundaryEquations", "=", 
   RowBox[{"{", "\[IndentingNewLine]", 
    RowBox[{
     RowBox[{"p1", "==", 
      RowBox[{"c1e", "-", 
       RowBox[{"Zc1e", " ", "q2"}]}]}], ",", "\[IndentingNewLine]", 
     RowBox[{"p2", "==", 
      RowBox[{"c2e", "+", 
       RowBox[{"Zc2e", " ", "q2"}]}]}]}], "\[IndentingNewLine]", "}"}]}], 
  ";"}]], "Input",
 CellChangeTimes->{{3.478679428921875*^9, 3.478679481265625*^9}, 
   3.4873877346662693`*^9, 3.4988885288318987`*^9, {3.5158210639861856`*^9, 
   3.51582106472056*^9}, {3.515900478739354*^9, 3.5159004792862253`*^9}, {
   3.515928580869215*^9, 3.515928582853654*^9}, 3.52577253333875*^9, {
   3.5719211535301576`*^9, 3.5719211557453613`*^9}, {3.573144594916039*^9, 
   3.57314462640184*^9}, 3.5731446879953628`*^9, {3.5731447690099964`*^9, 
   3.573144801970882*^9}, {3.5731515555661654`*^9, 3.5731515567032304`*^9}, {
   3.575862407130492*^9, 3.5758624079889097`*^9}, {3.5758624654873085`*^9, 
   3.5758624670012455`*^9}}],

Cell[BoxData[
 RowBox[{
  RowBox[{"systemVariables", "=", 
   RowBox[{"{", 
    RowBox[{"xv", ",", "q2", ",", "p1", ",", "p2"}], "}"}]}], ";"}]], "Input",
 CellChangeTimes->{
  3.504160940796875*^9, {3.504171522859375*^9, 3.504171524921875*^9}, {
   3.507570128828125*^9, 3.507570132078125*^9}, 3.50757021896875*^9, 
   3.507796195640625*^9, 3.507887067686471*^9, 3.571904675095819*^9}],

Cell[BoxData[
 RowBox[{
  RowBox[{"expressions", "=", 
   RowBox[{"{", 
    RowBox[{"q1", "\[Equal]", 
     RowBox[{"-", "q2"}]}], "}"}]}], ";"}]], "Input",
 CellChangeTimes->{{3.571904437694602*^9, 3.5719044499406233`*^9}}],

Cell[BoxData[
 RowBox[{
  RowBox[{"variableLimits", "=", 
   RowBox[{"{", 
    RowBox[{"{", 
     RowBox[{"xv", ",", "0.", ",", "Xvmax"}], "}"}], "}"}]}], ";"}]], "Input",
 CellChangeTimes->{3.5078869449067926`*^9}],

Cell[BoxData[
 RowBox[{
  RowBox[{"variableLowLimits", "=", 
   RowBox[{"{", 
    RowBox[{
     RowBox[{"{", 
      RowBox[{"p1", ",", "0"}], "}"}], ",", 
     RowBox[{"{", 
      RowBox[{"p2", ",", "0"}], "}"}]}], "}"}]}], ";"}]], "Input",
 CellChangeTimes->{{3.578505814681842*^9, 3.5785058445435495`*^9}, 
   3.578509359037567*^9}],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Compgen", "[", "file", "]"}]], "Input",
 CellChangeTimes->{3.5039025691670113`*^9}],

Cell[BoxData[
 RowBox[{
  StyleBox[
   RowBox[{"Part", "::", "partd"}], "MessageName"], 
  RowBox[{
  ":", " "}], "\<\"Part specification \[NoBreak]\\!\\(delayedPart \
\[LeftDoubleBracket] \\(\\(1, 1\\)\\) \[RightDoubleBracket]\\)\[NoBreak] is \
longer than depth of object. \\!\\(\\*ButtonBox[\\\"\[RightSkeleton]\\\", \
ButtonStyle->\\\"Link\\\", ButtonFrame->None, \
ButtonData:>\\\"paclet:ref/message/General/partd\\\", ButtonNote -> \
\\\"Part::partd\\\"]\\)\"\>"}]], "Message", "MSG",
 CellChangeTimes->{3.6211388917666492`*^9}],

Cell[BoxData[
 RowBox[{
  StyleBox[
   RowBox[{"XMLElement", "::", "cntsList"}], "MessageName"], 
  RowBox[{
  ":", " "}], "\<\"\[NoBreak]\\!\\(XMLElement[\\(\\(\\\"modelobject\\\", \
\\(\\({\\(\\(\\\"typename\\\" \[Rule] \\(\\(\\\"H\\\" \[Ellipsis] \
\\\"eG\\\"\\)\\)\\)\\), \\(\\(\[LeftSkeleton] 1 \
\[RightSkeleton]\\)\\)}\\)\\), \\(\\({\\(\\(XMLElement[\\(\\(\\\"icon\\\", \
\\(\\({\\(\\(\\\"isopath\\\" \[Rule] \
\\\"HydraulicPressureReducingValveG.svg\\\"\\)\\), \\(\\(\\\"iconrotation\\\" \
\[Rule] \\\"ON\\\"\\)\\), \\(\\(\\\"userpath\\\" \[Rule] \
\\\"HydraulicPressureReducingValveG.svg\\\"\\)\\)}\\)\\), \
\\(\\({}\\)\\)\\)\\)]\\)\\), \\(\\(XMLElement[\\(\\(\\\"portpositions\\\", \
\\(\\({}\\)\\), \\(\\({\\(\\(XMLElement[\\(\\(\\\"portpose\\\", \\(\\({\\(\\(\
\\\"x\\\" \[Rule] \\\"0\\\"\\)\\), \\(\\(\\\"y\\\" \[Rule] \
0.3333333333333333`\\)\\), \\(\\(\\\"a\\\" \[Rule] \\\"0\\\"\\)\\), \
\\(\\(\\\"name\\\" \[Rule] \\\"P1\\\"\\)\\)}\\)\\), \
\\(\\({}\\)\\)\\)\\)]\\)\\), \\(\\(\[LeftSkeleton] 3 \
\[RightSkeleton]\\)\\)}\\)\\)\\)\\)]\\)\\)}\\)\\)\\)\\)]\\)\[NoBreak] in \
\[NoBreak]\\!\\(XMLElement[\\(\\(\[LeftSkeleton] 1 \[RightSkeleton]\\)\\)]\\)\
\[NoBreak] is not a list of contents. The third item in an XMLElement must be \
a list of contents, even if it is an empty list. \\!\\(\\*ButtonBox[\\\"\
\[RightSkeleton]\\\", ButtonStyle->\\\"Link\\\", ButtonFrame->None, \
ButtonData:>\\\"paclet:ref/XMLElement\\\", ButtonNote -> \
\\\"XMLElement::cntsList\\\"]\\)\"\>"}]], "Message", "MSG",
 CellChangeTimes->{3.621138891787652*^9}],

Cell[BoxData[
 RowBox[{
  StyleBox[
   RowBox[{"Export", "::", "autofix"}], "MessageName"], 
  RowBox[{
  ":", " "}], "\<\"Malformed symbolic XML expression encountered. This may \
result in unexpected XML data. \\!\\(\\*ButtonBox[\\\"\[RightSkeleton]\\\", \
ButtonStyle->\\\"Link\\\", ButtonFrame->None, \
ButtonData:>\\\"paclet:ref/Export\\\", ButtonNote -> \\\"Export::autofix\\\"]\
\\)\"\>"}]], "Message", "MSG",
 CellChangeTimes->{3.6211388917906523`*^9}],

Cell[BoxData[
 RowBox[{
  StyleBox[
   RowBox[{"XMLElement", "::", "attrhs"}], "MessageName"], 
  RowBox[{
  ":", " "}], "\<\"\[NoBreak]\\!\\(0.3333333333333333`\\)\[NoBreak] in \
\[NoBreak]\\!\\(\\\"y\\\" \[Rule] 0.3333333333333333`\\)\[NoBreak] is not a \
valid value for an attribute in an XMLElement. The value of the attribute \
must be a string. \\!\\(\\*ButtonBox[\\\"\[RightSkeleton]\\\", \
ButtonStyle->\\\"Link\\\", ButtonFrame->None, \
ButtonData:>\\\"paclet:ref/XMLElement\\\", ButtonNote -> \
\\\"XMLElement::attrhs\\\"]\\)\"\>"}]], "Message", "MSG",
 CellChangeTimes->{3.621138891791652*^9}],

Cell[BoxData[
 RowBox[{
  StyleBox[
   RowBox[{"Export", "::", "autofix"}], "MessageName"], 
  RowBox[{
  ":", " "}], "\<\"Malformed symbolic XML expression encountered. This may \
result in unexpected XML data. \\!\\(\\*ButtonBox[\\\"\[RightSkeleton]\\\", \
ButtonStyle->\\\"Link\\\", ButtonFrame->None, \
ButtonData:>\\\"paclet:ref/Export\\\", ButtonNote -> \\\"Export::autofix\\\"]\
\\)\"\>"}]], "Message", "MSG",
 CellChangeTimes->{3.6211388917936525`*^9}],

Cell[BoxData[
 RowBox[{
  StyleBox[
   RowBox[{"XMLElement", "::", "attrhs"}], "MessageName"], 
  RowBox[{
  ":", " "}], "\<\"\[NoBreak]\\!\\(0.6666666666666666`\\)\[NoBreak] in \
\[NoBreak]\\!\\(\\\"y\\\" \[Rule] 0.6666666666666666`\\)\[NoBreak] is not a \
valid value for an attribute in an XMLElement. The value of the attribute \
must be a string. \\!\\(\\*ButtonBox[\\\"\[RightSkeleton]\\\", \
ButtonStyle->\\\"Link\\\", ButtonFrame->None, \
ButtonData:>\\\"paclet:ref/XMLElement\\\", ButtonNote -> \
\\\"XMLElement::attrhs\\\"]\\)\"\>"}]], "Message", "MSG",
 CellChangeTimes->{3.6211388917946525`*^9}],

Cell[BoxData[
 RowBox[{
  StyleBox[
   RowBox[{"Export", "::", "autofix"}], "MessageName"], 
  RowBox[{
  ":", " "}], "\<\"Malformed symbolic XML expression encountered. This may \
result in unexpected XML data. \\!\\(\\*ButtonBox[\\\"\[RightSkeleton]\\\", \
ButtonStyle->\\\"Link\\\", ButtonFrame->None, \
ButtonData:>\\\"paclet:ref/Export\\\", ButtonNote -> \\\"Export::autofix\\\"]\
\\)\"\>"}]], "Message", "MSG",
 CellChangeTimes->{3.6211388917956524`*^9}],

Cell[BoxData[
 RowBox[{
  StyleBox[
   RowBox[{"General", "::", "stop"}], "MessageName"], 
  RowBox[{
  ":", " "}], "\<\"Further output of \[NoBreak]\\!\\(\\*StyleBox[\\(Export :: \
autofix\\), \\\"MessageName\\\"]\\)\[NoBreak] will be suppressed during this \
calculation. \\!\\(\\*ButtonBox[\\\"\[RightSkeleton]\\\", \
ButtonStyle->\\\"Link\\\", ButtonFrame->None, \
ButtonData:>\\\"paclet:ref/message/General/stop\\\", ButtonNote -> \
\\\"General::stop\\\"]\\)\"\>"}]], "Message", "MSG",
 CellChangeTimes->{3.6211388917976527`*^9}],

Cell[BoxData[
 RowBox[{
  StyleBox[
   RowBox[{"XMLElement", "::", "attrhs"}], "MessageName"], 
  RowBox[{
  ":", " "}], "\<\"\[NoBreak]\\!\\(0.5`\\)\[NoBreak] in \[NoBreak]\\!\\(\\\"x\
\\\" \[Rule] 0.5`\\)\[NoBreak] is not a valid value for an attribute in an \
XMLElement. The value of the attribute must be a string. \
\\!\\(\\*ButtonBox[\\\"\[RightSkeleton]\\\", ButtonStyle->\\\"Link\\\", \
ButtonFrame->None, ButtonData:>\\\"paclet:ref/XMLElement\\\", ButtonNote -> \
\\\"XMLElement::attrhs\\\"]\\)\"\>"}]], "Message", "MSG",
 CellChangeTimes->{3.6211388917986526`*^9}],

Cell[BoxData[
 RowBox[{
  StyleBox[
   RowBox[{"General", "::", "stop"}], "MessageName"], 
  RowBox[{
  ":", " "}], "\<\"Further output of \
\[NoBreak]\\!\\(\\*StyleBox[\\(XMLElement :: attrhs\\), \
\\\"MessageName\\\"]\\)\[NoBreak] will be suppressed during this calculation. \
\\!\\(\\*ButtonBox[\\\"\[RightSkeleton]\\\", ButtonStyle->\\\"Link\\\", \
ButtonFrame->None, ButtonData:>\\\"paclet:ref/message/General/stop\\\", \
ButtonNote -> \\\"General::stop\\\"]\\)\"\>"}]], "Message", "MSG",
 CellChangeTimes->{3.6211388918006535`*^9}]
}, Open  ]],

Cell[BoxData[
 RowBox[{
  RowBox[{"kf", "=."}], ";", 
  RowBox[{"ke", "=."}], ";"}]], "Input",
 CellChangeTimes->{{3.5762415310479546`*^9, 3.5762415455559807`*^9}}]
}, Open  ]]
}, Open  ]]
},
WindowSize->{707, 505},
WindowMargins->{{Automatic, 207}, {Automatic, 181}},
FrontEndVersion->"8.0 for Microsoft Windows (64-bit) (October 6, 2011)",
StyleDefinitions->"Default.nb"
]
(* End of Notebook Content *)

(* Internal cache information *)
(*CellTagsOutline
CellTagsIndex->{}
*)
(*CellTagsIndex
CellTagsIndex->{}
*)
(*NotebookFileOutline
Notebook[{
Cell[CellGroupData[{
Cell[579, 22, 315, 4, 71, "Section"],
Cell[897, 28, 248, 4, 31, "Input"],
Cell[1148, 34, 694, 14, 52, "Input"],
Cell[CellGroupData[{
Cell[1867, 52, 100, 1, 36, "Subsection"],
Cell[1970, 55, 1527, 34, 172, "Input"],
Cell[3500, 91, 1015, 21, 92, "Input"],
Cell[4518, 114, 410, 10, 72, "Input"],
Cell[4931, 126, 427, 11, 72, "Input"],
Cell[5361, 139, 3785, 73, 252, "Input",
 CellGroupingRules->{GroupTogetherGrouping, 10000.}],
Cell[9149, 214, 162, 4, 31, "Input"],
Cell[9314, 220, 991, 20, 124, "Input"],
Cell[10308, 242, 424, 11, 52, "Input"],
Cell[10735, 255, 1344, 31, 102, "Input"],
Cell[12082, 288, 1011, 20, 92, "Input"],
Cell[13096, 310, 386, 8, 31, "Input"],
Cell[13485, 320, 224, 6, 31, "Input"],
Cell[13712, 328, 215, 6, 31, "Input"],
Cell[13930, 336, 334, 10, 31, "Input"],
Cell[CellGroupData[{
Cell[14289, 350, 107, 2, 31, "Input"],
Cell[14399, 354, 534, 11, 21, "Message"],
Cell[14936, 367, 1551, 26, 107, "Message"],
Cell[16490, 395, 460, 10, 21, "Message"],
Cell[16953, 407, 605, 12, 39, "Message"],
Cell[17561, 421, 460, 10, 21, "Message"],
Cell[18024, 433, 607, 12, 39, "Message"],
Cell[18634, 447, 460, 10, 21, "Message"],
Cell[19097, 459, 534, 11, 21, "Message"],
Cell[19634, 472, 575, 11, 39, "Message"],
Cell[20212, 485, 537, 11, 21, "Message"]
}, Open  ]],
Cell[20764, 499, 164, 4, 31, "Input"]
}, Open  ]]
}, Open  ]]
}
]
*)

(* End of internal cache information *)
